Given that D, E, and F are the midpoints of their respective sides, and AC = 24, what’s the length of DE¯¯¯¯¯¯¯¯?

An image of a triangle ABC. The midpoint of AB is labeled D, the midpoint of AC is labeled F, and the midpoint of BC is labeled E. Midsegments DE, EF, and FD are drawn. AC is labeled 24.

Question options:

2 units


6 units


12 units


4 units

=============================================

Explanation:

Refer to the diagram below. The goal is to find x, which is the horizontal distance from the base of the tree to the swing set.

Focus on triangle BCD.

The angle B is roughly 30.26 degrees, and this is the angle of depression. This is the amount of degrees Emir must look down (when starting at the horizontal) to spot the swing set.

We know that he's 14 ft off the ground, which explains why AB = CD = 14.

The goal is to find BC = AD = x.

---------------------------

Again, keep your focus on triangle BCD.

We'll use the tangent ratio to say

tan(angle) = opposite/adjacent

tan(B) = CD/BC

tan(30.26) = 14/x

x*tan(30.26) = 14

x = 14/tan(30.26)

x = 23.9965714046732

That value is approximate. Make sure your calculator is in degree mode.

That value rounds to 24 feet when rounding to the nearest whole foot.

Using the slope concept, it is found that the base of the treehouse is 24 feet from swingset.

In this problem:

Hence:

[tex]\tan{30.26^{\circ}} = \frac{14}{x}[/tex]

[tex]0.5834 = \frac{14}{x}[/tex]

[tex]x = \frac{14}{0.5834}[/tex]

[tex]x = 24[/tex]

The base of the treehouse is 24 feet from swingset.

You can learn more about the slope concept at brainly.com/question/18090623

Answer:

The possible approximate frequencies of the guitar string are 516.82 Hz and 508.82 Hz

Step-by-step explanation:

The given period of the tuning fork, T₁ = 1.95 × 10⁻³ s

The number of beats in 6.0 s = 24 beats

Therefore, the beat frequency, [tex]f_{beat}[/tex] = 4 beats per second = 4 Hz

Let f₁ represent the frequency of the tuning fork, and let f₂ represent the frequency of the guitar string, we have;

f₁ = 1/T₁ = 1/(1.95 × 10⁻³) ≈ 512.82 Hz

We have;

[tex]f_{beat} = \left | f_2 - f_1 \right |[/tex]

[tex]\pm f_{beat} = f_2 - f_1[/tex]

Therefore, we get;

[tex]4 \, Hz= \left | f_2 - 512.82 \, Hz \right |[/tex]

f₂ - 512.82 = ± 4

∴ f₂ = 512.82 ± 4

The possible frequencies of the guitar string,  f₂ ≈ 516.82 Hz or f₂ ≈ 508.82 Hz

Answer:

70

Step-by-step explanation:

we have the angle of vertex in the isosceles triangle = 180-2*bottom coner= 180-65/2=50

3 angles in the equilateral triangle are equal to 60

we have 50 + 60 +h =the angle of PQR =180

h=70

Answer: h = 70°

In the triangle with Angle R = 65

It is a isoceles triangle as two sides are equal

So base angles will be equall too

Then the third angle will which is the q one will be

65+65+q = 180

q = 180 - 130

q = 50

In the other triangle with all sides equal will be equilateral triangle which means all angles equal = 60

So

Now ATQ

60 + 50 + h = 180

h = 180 - 110 (Angles on a straight line adds upto 180)

h = 70

Must click thanks and mark brainliest

Answer:

1

Step-by-step explanation:

add 1/2 + 1/2 = 2/2 = 1

Answer:

a) x=3

b) x=4.5

Step-by-step explanation:

2(5x – 3) = 24

10x-6=24

10x=30

x=3

5(2x + 1) = 50

10x+5=50

10x=45

x=4.5

Answer:

The answer is $2.50

Answer:

the answer would be c because c= $2.50

Step-by-step explanation:

Answer:

x ≈ 94.4

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan58° = [tex]\frac{LM}{KL}[/tex] = [tex]\frac{x}{59}[/tex] ( multiply both sides by 59 )

59 × tan58° = x , then

x ≈ 94.4 ( to the nearest tenth )

Answer:

<a=32

<b=40

<c=40

Step-by-step explanation:

to find angle a you have to subtract the 50 minus 180 to find the angle close to the 50 because angles in a straight line add up to 180. the answer will be

180-50=130

after finding the angle in that triangle you must add it to the other angle present which is 18° then subtract by 180 because angles in a straight line add up to 180

130+18+a=180

a=180-148

a=32 and that's how you find a

to find b you must know that the angle at the center is twice the angle at the circumference meaning the large angle C is 90°,now if it's 90° inorder to find the big angle B you must add the 18+90 then subtract 180

18+90+B=180

B=180-108

=72

since the combination of angle a and b will give you 72 you can find angle c by subtracting a from 72

c=72-32

=40

then if you look at angle c and angle b you can tell that they are alternating meaning angle b is also 40

I hope this helps

9/x and 20x⁹ are the monomials.

The correct option A and D.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

A monomial is a polynomial with just one term.

From the given choices:

9/x and 20x⁹ are the monomials.

11x - 9 and 20x⁹ -7x are the binomial.

Therefore, A and D are the monomials.

To learn more about the Polynomials;

brainly.com/question/11536910

#SPJ1

Answer:

Do you need it in percentage, a graph or just normal annual calculation?

Answer:

she saves $24 dollars every month. 36 + 24 =60 +24 =84 +24 =108 +24 =132 :)

Answer:

43.49

Step-by-step explanation:

let his normal hourly rate be x

16x+7x/2=848

39x/2=848

x=848 ÷ 39/2

=43.48717

Answer:

for every minute it will cost 3 dollars

Step-by-step explanation:

c(x)=3x+2.00

The cost to get in the taxi is 2 dollars

The slope is 3

3x means that for every minute it will cost 3 dollars

Answer:

Step-by-step explanation:

y = 600 * (1.04)¹⁵

= 600 * 1.80094351

= $ 1080.57

Answer: [tex]60\ ft[/tex]

Step-by-step explanation:

Given

Side length of square shape [tex]a=15\ ft[/tex]

Length of the garden is equal to the perimeter of the square i.e. 4 times the side length

[tex]\Rightarrow \text{Lenght L= }4a\\\Rightarrow L=4\times 15\\\Rightarrow L=60\ ft[/tex]

Thus, the length of the require garden is [tex]60\ ft[/tex]

Answer:

(2,1)

Step-by-step explanation:

2x - 2y = 2

5x + 2y = 12

again just add them in this case

7x = 14

x = 2

4 - 2y = 2

-2y = -2

y = 1

Answer:

C

Step-by-step explanation:

Given

[tex]\frac{x^2-16}{(x-16)(x+4)}[/tex]

The numerator is a difference of squares

x² - 16 = (x - 4)(x + 4)

= [tex]\frac{(x-4)(x+4)}{(x-16)(x+4) }[/tex] ← cancel the common factor (x + 4) on numerator/ denominator

= [tex]\frac{x-4}{x-16}[/tex] → C

Answer:

Step-by-step explanation:

-4 and -3

Answer:

-4 and 3 because I tookt the test and the other guy was right too

Answer:

26 sqrt(5) + 2 sqrt(10)

Step-by-step explanation:

2 sqrt(5) *(13+sqrt(2))

Distribute

26 sqrt(5) + 2 sqrt(10)

Answer:

[tex]26\sqrt5 +2 \sqrt10[/tex]

Step-by-step explanation:

Answer:

ratio of Sophia's sweets to Isabel's sweets is

13:8

Answer:

you first have to find the number of sweets that sophia got.by subtracting the total number of sweets minus the number of sweets that isabel got which will be

42-16=26

therefore the ratio will be

16:26

8:13

I hope this helps

Answer:

the time taken for the 15 people to drink 155 pints is 20.67 min.

Step-by-step explanation:

Given;

10 people took 5 mins to drink 25 pints of water

[tex]The \ rate\ for \ 10 \ people = \frac{25 \ pints }{5 \ mins} = 5 \ \frac{pints}{\min} \\\\The \ rate \ for \ 1 \ person = \frac{5}{10} \ \frac{pints}{\min} = 0.5 \ \frac{pints}{\min} \\\\The \ rate \ for \ 15 \ people = 15( 0.5 \ \frac{pints}{\min} )= 7.5 \ \frac{pints}{\min} \\\\Time \ taken \ for \ the \ 15 \ people \ to \ drink \ 155 \ pints = \frac{155 \ pints}{7.5 \ pints/ \min} \\\\= 20.67 \min[/tex]

Therefore, the time taken for the 15 people to drink 155 pints is 20.67 min.

Answer:

7 : 5

Step-by-step explanation:

number of females = 3540 - 2065 = 1475

males : females

2065 : 1475

7 : 5

Answer:

3.25 minutes

Step-by-step explanation:

3.25 minutes per green light x 24 = 78

the yellow light is a given, hence 6 cars pass through

78 + 6 = 84 cars

Answer:

5

Step-by-step explanation:

45=3×3×5

If we multiply by 5 it becomes a perfect square.

Answer:

2 1/4 cups.

Step-by-step explanation:

If we want to find the total amount of cheese Belle used, we have to add the number of cups of cheddar and parmesan together:

2 + 1/4 = 2 1/4

Therefore, our answer is 2 1/4, specifically, 2 1/4 cups.

Answer:

11.3

Step-by-step explanation:

a = AC × sin(A)/sin(B)

Now <A =180-25-48 = 107

a = 5×sin(107)/sin(25)

a ≈ 11.3

Answered by GAUTHMATH

Answer:

B

Step-by-step explanation:

Sin x°= opposite ÷ hypotenuse

Cos x°= adjacent ÷ hypotenuse

Tan x°= opposite ÷ adjacent

Ctg x°= adjacent ÷ opposite

The correct will bet cot x = adjacent ÷ opposite

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Using trigonometric properties we have

Learn more about trigonometry here:

https://brainly.com/question/17103461

#SPJ5

Answer:

-31  

Step-by-step explanation:

2x - abs(4 - 7x)

2x = 2 * - 3 = - 6

4 - 7x = 4 - 7*-3 = 4 + 21 = 25

-6 - abs(25)

-6 - 25 = -31

You should note three things.

1. the absolute value of 25 is 25

2. There is a - sign outside the influence of the 25 so 25 becomes - 25

3. - 6 - 25 = - 31

Answer:

7/60

Step-by-step explanation:

Because the question is phrased such that it asks "the ratio of time with father to....", we know to put the time with father on top, or first. Similarly, since it is asked to put the ratio of time with the father to the time in daycare, we can put the daycare amount second/on the bottom. Therefore, we can write the ratio as

(42 minutes)/(6 hours)

To make both of these in terms of minutes to simplify it, we know that 60 minutes = 1 hour, so 1 hour / 60 minutes =1 . Since multiplying something by 1 keeps it the same, we can multiply our ratio by this amount. We want to multiply with the hour on top so the hours cancel out, as so:

[tex]\frac{42 minutes}{6 hours} * \frac{1 hour}{60 minutes} = \frac{42 minutes * hours}{360 minutes * hours} = \frac{42}{360}[/tex]

To simplify this even further, we can note that 6 is a factor of both 42 and 360*, so we can multiply this fraction by (1/6) / (1/6) to get

(42/360) * (1/6)/(1/6) = 7/60 as our final answer

If this doesn't come up immediately, you can always find the greatest common factor by listing the factors of each number and finding the highest one that fits both, e.g.

for 42: 42, 21, 14, 7 , 6...

for 360: 360,180, ... 6,5....